Problem: Multiply the following complex numbers: $({-2i}) \cdot ({-3-5i})$
Explanation: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-2i}) \cdot ({-3-5i}) = $ $ ({0} \cdot {-3}) + ({0} \cdot {-5}i) + ({-2}i \cdot {-3}) + ({-2}i \cdot {-5}i) $ Then simplify the terms: $ (0) + (0i) + (6i) + (10 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ 0 + (0 + 6)i + 10i^2 $ After we plug in $i^2 = -1$ , the result becomes $ 0 + (0 + 6)i - 10 $ The result is simplified: $ (0 - 10) + (6i) = -10+6i $